{"id":15953,"date":"2024-01-19T02:37:12","date_gmt":"2024-01-18T23:07:12","guid":{"rendered":"https:\/\/rasanegar.com\/blog\/%d8%a7%d8%af%d8%ba%d8%a7%d9%85-%d9%85%d8%b1%d8%aa%d8%a8-%d8%b3%d8%a7%d8%b2%db%8c-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86\/"},"modified":"2024-01-19T02:37:12","modified_gmt":"2024-01-18T23:07:12","slug":"%d8%a7%d8%af%d8%ba%d8%a7%d9%85-%d9%85%d8%b1%d8%aa%d8%a8-%d8%b3%d8%a7%d8%b2%db%8c-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86","status":"publish","type":"post","link":"https:\/\/rasanegaar.com\/blog\/%d8%a7%d8%af%d8%ba%d8%a7%d9%85-%d9%85%d8%b1%d8%aa%d8%a8-%d8%b3%d8%a7%d8%b2%db%8c-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86\/","title":{"rendered":"\u0627\u062f\u063a\u0627\u0645 \u0645\u0631\u062a\u0628 \u0633\u0627\u0632\u06cc \u062f\u0631 \u067e\u0627\u06cc\u062a\u0648\u0646"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_85 counter-hierarchy ez-toc-counter ez-toc-custom ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\"><p class=\"ez-toc-title\" style=\"cursor:inherit\">\u0633\u0631\u0641\u0635\u0644\u0647\u0627\u06cc \u0645\u0637\u0644\u0628<\/p>\n<\/div><nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/rasanegaar.com\/blog\/%d8%a7%d8%af%d8%ba%d8%a7%d9%85-%d9%85%d8%b1%d8%aa%d8%a8-%d8%b3%d8%a7%d8%b2%db%8c-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86\/#%d9%85%d8%b9%d8%b1%d9%81%db%8c\" >\u0645\u0639\u0631\u0641\u06cc<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/rasanegaar.com\/blog\/%d8%a7%d8%af%d8%ba%d8%a7%d9%85-%d9%85%d8%b1%d8%aa%d8%a8-%d8%b3%d8%a7%d8%b2%db%8c-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86\/#%d8%a7%db%8c%d8%af%d9%87_%d9%be%d8%b4%d8%aa_%d9%85%d8%b1%d8%aa%d8%a8_%d8%b3%d8%a7%d8%b2%db%8c_%d8%a7%d8%af%d8%ba%d8%a7%d9%85\" >\u0627\u06cc\u062f\u0647 \u067e\u0634\u062a \u0645\u0631\u062a\u0628 \u0633\u0627\u0632\u06cc \u0627\u062f\u063a\u0627\u0645<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/rasanegaar.com\/blog\/%d8%a7%d8%af%d8%ba%d8%a7%d9%85-%d9%85%d8%b1%d8%aa%d8%a8-%d8%b3%d8%a7%d8%b2%db%8c-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86\/#%d8%b1%d9%88%d8%b4_%d9%be%db%8c%d8%a7%d8%af%d9%87_%d8%b3%d8%a7%d8%b2%db%8c_merge_sort_%d8%af%d8%b1_%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86\" >\u0631\u0648\u0634 \u067e\u06cc\u0627\u062f\u0647 \u0633\u0627\u0632\u06cc Merge Sort \u062f\u0631 \u067e\u0627\u06cc\u062a\u0648\u0646<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/rasanegaar.com\/blog\/%d8%a7%d8%af%d8%ba%d8%a7%d9%85-%d9%85%d8%b1%d8%aa%d8%a8-%d8%b3%d8%a7%d8%b2%db%8c-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86\/#%d8%a8%d9%87%db%8c%d9%86%d9%87_%d8%b3%d8%a7%d8%b2%db%8c\" >\u0628\u0647\u06cc\u0646\u0647 \u0633\u0627\u0632\u06cc<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/rasanegaar.com\/blog\/%d8%a7%d8%af%d8%ba%d8%a7%d9%85-%d9%85%d8%b1%d8%aa%d8%a8-%d8%b3%d8%a7%d8%b2%db%8c-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86\/#%d9%86%d8%aa%db%8c%d8%ac%d9%87\" >\u0646\u062a\u06cc\u062c\u0647<\/a><\/li><\/ul><\/nav><\/div>\n<span class=\"span-reading-time rt-reading-time\" style=\"display: block;\"><span class=\"rt-label rt-prefix\">\u0632\u0645\u0627\u0646 \u0644\u0627\u0632\u0645 \u0628\u0631\u0627\u06cc \u0645\u0637\u0627\u0644\u0639\u0647: <\/span> <span class=\"rt-time\"> 8<\/span> <span class=\"rt-label rt-postfix\">\u062f\u0642\u06cc\u0642\u0647<\/span><\/span><p> <br \/>\n<\/p>\n<div><noscript><\/noscript><\/p>\n<h3 id=\"introduction\"><span class=\"ez-toc-section\" id=\"%d9%85%d8%b9%d8%b1%d9%81%db%8c\"><\/span>\u0645\u0639\u0631\u0641\u06cc<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Merge Sort \u06cc\u06a9\u06cc \u0627\u0632 \u0645\u0639\u0631\u0648\u0641 \u062a\u0631\u06cc\u0646 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0647\u0627\u06cc \u0645\u0631\u062a\u0628 \u0633\u0627\u0632\u06cc \u0627\u0633\u062a.  \u0627\u06af\u0631 \u062f\u0631 \u062d\u0627\u0644 \u062a\u062d\u0635\u06cc\u0644 \u062f\u0631 \u0631\u0634\u062a\u0647 \u06a9\u0627\u0645\u067e\u06cc\u0648\u062a\u0631 \u0647\u0633\u062a\u06cc\u062f\u060c <em>\u0627\u062f\u063a\u0627\u0645 \u0645\u0631\u062a\u0628 \u0633\u0627\u0632\u06cc<\/em>\u060c \u062f\u0631 \u06a9\u0646\u0627\u0631 Quick Sort \u0627\u062d\u062a\u0645\u0627\u0644\u0627\u064b \u0627\u0648\u0644\u06cc\u0646 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0645\u0631\u062a\u0628 \u0633\u0627\u0632\u06cc \u06a9\u0627\u0631\u0622\u0645\u062f \u0648 \u0647\u0645\u0647 \u0645\u0646\u0638\u0648\u0631\u0647 \u0627\u06cc \u0627\u0633\u062a \u06a9\u0647 \u0646\u0627\u0645 \u0622\u0646 \u0631\u0627 \u0634\u0646\u06cc\u062f\u0647 \u0627\u06cc\u062f.  \u0647\u0645\u0686\u0646\u06cc\u0646 \u06cc\u06a9 \u0646\u0645\u0648\u0646\u0647 \u06a9\u0644\u0627\u0633\u06cc\u06a9 \u0627\u0632 a \u0627\u0633\u062a <em>\u062a\u0641\u0631\u0642\u0647 \u0628\u06cc\u0646\u062f\u0627\u0632 \u0648 \u062d\u06a9\u0648\u0645\u062a \u06a9\u0646<\/em> \u062f\u0633\u062a\u0647 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0647\u0627<\/p>\n<h3 id=\"theideabehindthemergesort\"><span class=\"ez-toc-section\" id=\"%d8%a7%db%8c%d8%af%d9%87_%d9%be%d8%b4%d8%aa_%d9%85%d8%b1%d8%aa%d8%a8_%d8%b3%d8%a7%d8%b2%db%8c_%d8%a7%d8%af%d8%ba%d8%a7%d9%85\"><\/span>\u0627\u06cc\u062f\u0647 \u067e\u0634\u062a \u0645\u0631\u062a\u0628 \u0633\u0627\u0632\u06cc \u0627\u062f\u063a\u0627\u0645<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u0631\u0648\u0634 \u0627\u062f\u063a\u0627\u0645 \u0645\u0631\u062a\u0628 \u0633\u0627\u0632\u06cc \u0628\u0647 \u0627\u06cc\u0646 \u0635\u0648\u0631\u062a \u0627\u0633\u062a:<\/p>\n<ul>\n<li>\n<p>\u06cc\u06a9 \u0622\u0631\u0627\u06cc\u0647 \u0627\u0648\u0644\u06cc\u0647 \u0628\u0647 \u062f\u0648 \u0642\u0633\u0645\u062a \u062a\u0642\u0631\u06cc\u0628\u0627\u064b \u0645\u0633\u0627\u0648\u06cc \u062a\u0642\u0633\u06cc\u0645 \u0645\u06cc \u0634\u0648\u062f.  \u0627\u06af\u0631 \u0622\u0631\u0627\u06cc\u0647 \u062f\u0627\u0631\u0627\u06cc \u062a\u0639\u062f\u0627\u062f \u0641\u0631\u062f \u0639\u0646\u0635\u0631 \u0628\u0627\u0634\u062f\u060c \u06cc\u06a9\u06cc \u0627\u0632 \u0622\u0646 &#8220;\u0646\u06cc\u0645\u0647 \u0647\u0627&#8221; \u06cc\u06a9 \u0639\u0646\u0635\u0631 \u0628\u0632\u0631\u06af\u062a\u0631 \u0627\u0632 \u062f\u06cc\u06af\u0631\u06cc \u0627\u0633\u062a.<\/p>\n<\/li>\n<li>\n<p>\u0632\u06cc\u0631\u0622\u0631\u0627\u06cc\u0647 \u0647\u0627 \u0628\u0627\u0631\u0647\u0627 \u0648 \u0628\u0627\u0631\u0647\u0627 \u0628\u0647 \u062f\u0648 \u0646\u06cc\u0645 \u062a\u0642\u0633\u06cc\u0645 \u0645\u06cc \u0634\u0648\u0646\u062f \u062a\u0627 \u0627\u06cc\u0646\u06a9\u0647 \u0628\u0647 \u0622\u0631\u0627\u06cc\u0647 \u0647\u0627\u06cc\u06cc \u0628\u0631\u0633\u06cc\u062f \u06a9\u0647 \u0647\u0631 \u06a9\u062f\u0627\u0645 \u0641\u0642\u0637 \u06cc\u06a9 \u0639\u0646\u0635\u0631 \u062f\u0627\u0631\u0646\u062f.<\/p>\n<\/li>\n<li>\n<p>\u0633\u067e\u0633 \u062c\u0641\u062a\u200c\u0647\u0627\u06cc \u0622\u0631\u0627\u06cc\u0647\u200c\u0647\u0627\u06cc \u06cc\u06a9 \u0639\u0646\u0635\u0631\u06cc \u0631\u0627 \u062f\u0631 \u0622\u0631\u0627\u06cc\u0647\u200c\u0647\u0627\u06cc \u062f\u0648 \u0639\u0646\u0635\u0631\u06cc \u062a\u0631\u06a9\u06cc\u0628 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u062f \u0648 \u0622\u0646\u0647\u0627 \u0631\u0627 \u062f\u0631 process.  \u0633\u067e\u0633 \u0627\u06cc\u0646 \u062c\u0641\u062a \u0647\u0627\u06cc \u0645\u0631\u062a\u0628 \u0634\u062f\u0647 \u062f\u0631 \u0622\u0631\u0627\u06cc\u0647 \u0647\u0627\u06cc \u0686\u0647\u0627\u0631 \u0639\u0646\u0635\u0631\u06cc \u0627\u062f\u063a\u0627\u0645 \u0645\u06cc \u0634\u0648\u0646\u062f \u0648 \u0628\u0647 \u0647\u0645\u06cc\u0646 \u062a\u0631\u062a\u06cc\u0628 \u0631\u0648\u06cc \u062a\u0627 \u0632\u0645\u0627\u0646\u06cc \u06a9\u0647 \u062f\u0631 \u0646\u0647\u0627\u06cc\u062a \u0622\u0631\u0627\u06cc\u0647 \u0627\u0648\u0644\u06cc\u0647 \u0645\u0631\u062a\u0628 \u0634\u062f\u0647 \u0628\u0627\u0634\u062f.<\/p>\n<\/li>\n<\/ul>\n<p>\u062f\u0631 \u0627\u06cc\u0646\u062c\u0627 \u06cc\u06a9 \u062a\u062c\u0633\u0645 \u0627\u0632 Merge Sort \u0627\u0633\u062a:<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/rasanegar.com\/blog\/wp-content\/uploads\/2024\/01\/marge-sort-in-python-01.png\" alt=\"\u0627\u062f\u063a\u0627\u0645 - \u0645\u0631\u062a\u0628 \u06a9\u0631\u062f\u0646 -python-01.png\" title=\"\"><\/p>\n<p>\u0647\u0645\u0627\u0646\u0637\u0648\u0631 \u06a9\u0647 \u0645\u06cc \u0628\u06cc\u0646\u06cc\u062f\u060c \u0627\u06cc\u0646 \u0648\u0627\u0642\u0639\u06cc\u062a \u06a9\u0647 \u0622\u0631\u0627\u06cc\u0647 \u0631\u0627 \u0646\u0645\u06cc \u062a\u0648\u0627\u0646 \u0628\u0647 \u0646\u06cc\u0645\u0647 \u0647\u0627\u06cc \u0645\u0633\u0627\u0648\u06cc \u062a\u0642\u0633\u06cc\u0645 \u06a9\u0631\u062f \u0645\u0634\u06a9\u0644\u06cc \u0646\u06cc\u0633\u062a\u060c <em>3<\/em> \u0641\u0642\u0637 &#8220;\u0645\u0646\u062a\u0638\u0631&#8221; \u0645\u06cc \u0634\u0648\u062f \u062a\u0627 \u0645\u0631\u062a\u0628 \u0633\u0627\u0632\u06cc \u0622\u063a\u0627\u0632 \u0634\u0648\u062f.<\/p>\n<p>\u062f\u0648 \u0631\u0627\u0647 \u0627\u0635\u0644\u06cc \u0628\u0631\u0627\u06cc \u067e\u06cc\u0627\u062f\u0647 \u0633\u0627\u0632\u06cc \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 Merge Sort \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f\u060c \u06cc\u06a9\u06cc \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 a <strong><em>\u0628\u0627\u0644\u0627 \u067e\u0627\u06cc\u06cc\u0646<\/em> \u0631\u0648\u06cc\u06a9\u0631\u062f<\/strong> \u0645\u0627\u0646\u0646\u062f \u0645\u062b\u0627\u0644 \u0628\u0627\u0644\u0627\u060c \u06a9\u0647 \u0645\u0631\u062a\u0628 \u0633\u0627\u0632\u06cc \u0627\u062f\u063a\u0627\u0645 \u0627\u063a\u0644\u0628 \u0628\u0647 \u0627\u06cc\u0646 \u0635\u0648\u0631\u062a \u0627\u0633\u062a.<\/p>\n<p>\u0631\u0648\u06cc\u06a9\u0631\u062f \u062f\u06cc\u06af\u0631\u060c \u06cc\u0639\u0646\u06cc <strong><em>\u0627\u0632 \u067e\u0627\u06cc\u06cc\u0646 \u0628\u0647 \u0628\u0627\u0644\u0627<\/em><\/strong>\u060c \u062f\u0631 \u062c\u0647\u062a \u0645\u062e\u0627\u0644\u0641 \u06a9\u0627\u0631 \u0645\u06cc \u06a9\u0646\u062f\u060c \u0628\u062f\u0648\u0646 \u0628\u0627\u0632\u06af\u0634\u062a (\u0628\u0647 \u0635\u0648\u0631\u062a \u062a\u06a9\u0631\u0627\u0631\u06cc \u06a9\u0627\u0631 \u0645\u06cc \u06a9\u0646\u062f) &#8211; \u0627\u06af\u0631 \u0622\u0631\u0627\u06cc\u0647 \u0645\u0627 \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u062f <em>\u0646<\/em> \u0639\u0646\u0627\u0635\u0631\u06cc \u06a9\u0647 \u0622\u0646 \u0631\u0627 \u0628\u0647 \u0622\u0646\u0647\u0627 \u062a\u0642\u0633\u06cc\u0645 \u0645\u06cc \u06a9\u0646\u06cc\u0645 <em>\u0646<\/em> \u0632\u06cc\u0631\u0622\u0631\u0627\u06cc\u0647 \u0647\u0627\u06cc \u06cc\u06a9 \u0639\u0646\u0635\u0631 \u0648 \u0645\u0631\u062a\u0628 \u0633\u0627\u0632\u06cc \u062c\u0641\u062a \u0622\u0631\u0627\u06cc\u0647 \u0647\u0627\u06cc \u06cc\u06a9 \u0639\u0646\u0635\u0631\u06cc \u0645\u062c\u0627\u0648\u0631\u060c \u0633\u067e\u0633 \u0645\u0631\u062a\u0628 \u0633\u0627\u0632\u06cc \u062c\u0641\u062a \u0647\u0627\u06cc \u0645\u062c\u0627\u0648\u0631 \u0627\u0632 \u0622\u0631\u0627\u06cc\u0647 \u0647\u0627\u06cc \u062f\u0648 \u0639\u0646\u0635\u0631\u06cc \u0648 \u063a\u06cc\u0631\u0647 \u0631\u0648\u06cc.<\/p>\n<div class=\"alert alert-note\">\n<div class=\"flex\">\n<div class=\"flex-shrink-0 mr-3\"><\/div>\n<div class=\"w-full\">\n<p><strong>\u062a\u0648\u062c\u0647 \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u06cc\u062f:<\/strong> \u0627\u06cc\u0646 <em>\u0627\u0632 \u067e\u0627\u06cc\u06cc\u0646 \u0628\u0647 \u0628\u0627\u0644\u0627<\/em> \u0631\u0648\u06cc\u06a9\u0631\u062f \u0628\u0647\u06cc\u0646\u0647 \u0633\u0627\u0632\u06cc \u062c\u0627\u0644\u0628\u06cc \u0631\u0627 \u0627\u0631\u0627\u0626\u0647 \u0645\u06cc \u062f\u0647\u062f \u06a9\u0647 \u062f\u0631 \u0645\u0648\u0631\u062f \u0622\u0646 \u0628\u062d\u062b \u062e\u0648\u0627\u0647\u06cc\u0645 \u06a9\u0631\u062f <a href=\"#optimization\" class=\"broken_link\">\u0628\u0639\u062f<\/a>.  \u0645\u0627 \u0627\u062c\u0631\u0627 \u062e\u0648\u0627\u0647\u06cc\u0645 \u06a9\u0631\u062f <em>\u0628\u0627\u0644\u0627 \u067e\u0627\u06cc\u06cc\u0646<\/em> \u0631\u0648\u06cc\u06a9\u0631\u062f \u0633\u0627\u062f\u0647\u200c\u062a\u0631 \u0648 \u0634\u0647\u0648\u062f\u06cc\u200c\u062a\u0631 \u0647\u0645\u0631\u0627\u0647 \u0628\u0627 \u0627\u06cc\u0646 \u0648\u0627\u0642\u0639\u06cc\u062a \u0627\u0633\u062a \u06a9\u0647 \u0647\u06cc\u0686 \u062a\u0641\u0627\u0648\u062a \u0648\u0627\u0642\u0639\u06cc \u0628\u06cc\u0646 \u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0632\u0645\u0627\u0646\u06cc \u0628\u06cc\u0646 \u0622\u0646\u0647\u0627 \u0628\u062f\u0648\u0646 \u0628\u0647\u06cc\u0646\u0647\u200c\u0633\u0627\u0632\u06cc \u062e\u0627\u0635 \u0648\u062c\u0648\u062f \u0646\u062f\u0627\u0631\u062f.<\/p>\n<\/p><\/div><\/div><\/div>\n<p>\u0628\u062e\u0634 \u0627\u0635\u0644\u06cc \u0647\u0631 \u062f\u0648 \u0627\u06cc\u0646 \u0631\u0648\u06cc\u06a9\u0631\u062f \u0627\u06cc\u0646 \u0627\u0633\u062a \u06a9\u0647 \u0686\u06af\u0648\u0646\u0647 \u062f\u0648 \u0622\u0631\u0627\u06cc\u0647 \u06a9\u0648\u0686\u06a9\u062a\u0631 \u0631\u0627 \u062f\u0631 \u06cc\u06a9 \u0622\u0631\u0627\u06cc\u0647 \u0628\u0632\u0631\u06af\u062a\u0631 \u062a\u0631\u06a9\u06cc\u0628 \u0645\u06cc \u06a9\u0646\u06cc\u0645 (\u0627\u062f\u063a\u0627\u0645 \u0645\u06cc \u06a9\u0646\u06cc\u0645).  \u0627\u06cc\u0646 \u06a9\u0627\u0631 \u06a9\u0627\u0645\u0644\u0627\u064b \u0634\u0647\u0648\u062f\u06cc \u0627\u0646\u062c\u0627\u0645 \u0645\u06cc \u0634\u0648\u062f\u060c \u0641\u0631\u0636 \u06a9\u0646\u06cc\u062f \u0622\u062e\u0631\u06cc\u0646 \u0645\u0631\u062d\u0644\u0647 \u0631\u0627 \u062f\u0631 \u0645\u062b\u0627\u0644 \u0642\u0628\u0644\u06cc \u062e\u0648\u062f \u0628\u0631\u0631\u0633\u06cc \u0645\u06cc \u06a9\u0646\u06cc\u0645.  \u0645\u0627 \u0622\u0631\u0627\u06cc\u0647 \u0647\u0627 \u0631\u0627 \u062f\u0627\u0631\u06cc\u0645:<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/rasanegar.com\/blog\/wp-content\/uploads\/2024\/01\/marge-sort-in-python-02.png\" alt=\"\u0627\u062f\u063a\u0627\u0645 - \u0645\u0631\u062a\u0628 \u06a9\u0631\u062f\u0646 -python-02.png\" title=\"\"><\/p>\n<p>\u0627\u0648\u0644\u06cc\u0646 \u06a9\u0627\u0631\u06cc \u06a9\u0647 \u0627\u0646\u062c\u0627\u0645 \u0645\u06cc \u062f\u0647\u06cc\u0645 \u0627\u06cc\u0646 \u0627\u0633\u062a \u06a9\u0647 \u0628\u0647 \u0639\u0646\u0635\u0631 \u0627\u0648\u0644 \u0647\u0631 \u062f\u0648 \u0622\u0631\u0627\u06cc\u0647 \u0646\u06af\u0627\u0647 \u06a9\u0646\u06cc\u0645.  \u0645\u0627 \u06cc\u06a9\u06cc \u0631\u0627 \u067e\u06cc\u062f\u0627 \u0645\u06cc \u06a9\u0646\u06cc\u0645 \u06a9\u0647 \u06a9\u0648\u0686\u06a9\u062a\u0631 \u0627\u0633\u062a\u060c \u062f\u0631 \u0645\u0648\u0631\u062f \u0645\u0627 \u0627\u06cc\u0646\u0637\u0648\u0631 \u0627\u0633\u062a <em>1<\/em>\u060c \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646 \u0627\u0648\u0644\u06cc\u0646 \u0639\u0646\u0635\u0631 \u0622\u0631\u0627\u06cc\u0647 \u0645\u0631\u062a\u0628 \u0634\u062f\u0647 \u0645\u0627 \u0627\u0633\u062a\u060c \u0648 \u062f\u0631 \u0642\u0633\u0645\u062a \u062c\u0644\u0648 \u062d\u0631\u06a9\u062a \u0645\u06cc \u06a9\u0646\u06cc\u0645 <em>\u0628<\/em> \u0622\u0631\u0627\u06cc\u0647:<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/rasanegar.com\/blog\/wp-content\/uploads\/2024\/01\/marge-sort-in-python-03.png\" alt=\"\u0627\u062f\u063a\u0627\u0645 - \u0645\u0631\u062a\u0628 \u06a9\u0631\u062f\u0646 -python-03.png\" title=\"\"><\/p>\n<p>\u0633\u067e\u0633 \u0628\u0647 \u062c\u0641\u062a \u0639\u0646\u0627\u0635\u0631 \u0628\u0639\u062f\u06cc \u0646\u06af\u0627\u0647 \u0645\u06cc \u06a9\u0646\u06cc\u0645 <em>2<\/em> \u0648 <em>3<\/em>; <em>2<\/em> \u06a9\u0648\u0686\u06a9\u062a\u0631 \u0627\u0633\u062a\u060c \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646 \u0622\u0646 \u0631\u0627 \u062f\u0631 \u0622\u0631\u0627\u06cc\u0647 \u0645\u0631\u062a\u0628 \u0634\u062f\u0647 \u062e\u0648\u062f \u0642\u0631\u0627\u0631 \u0645\u06cc \u062f\u0647\u06cc\u0645 \u0648 \u062f\u0631 \u0622\u0631\u0627\u06cc\u0647 \u0628\u0647 \u062c\u0644\u0648 \u062d\u0631\u06a9\u062a \u0645\u06cc \u06a9\u0646\u06cc\u0645 <em>\u0622<\/em>.  \u0627\u0644\u0628\u062a\u0647 \u062f\u0631 \u0622\u0631\u0627\u06cc\u0647 \u062c\u0644\u0648 \u0646\u0645\u06cc \u0631\u0648\u06cc\u0645 <em>\u0628<\/em> \u0648 \u0645\u0627 \u0646\u0634\u0627\u0646\u06af\u0631 \u062e\u0648\u062f \u0631\u0627 \u0646\u06af\u0647 \u0645\u06cc \u062f\u0627\u0631\u06cc\u0645 <em>3<\/em> \u0628\u0631\u0627\u06cc \u0645\u0642\u0627\u06cc\u0633\u0647 \u0647\u0627\u06cc \u0622\u06cc\u0646\u062f\u0647:<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/rasanegar.com\/blog\/wp-content\/uploads\/2024\/01\/marge-sort-in-python-04.png\" alt=\"\u0627\u062f\u063a\u0627\u0645 - \u0645\u0631\u062a\u0628 \u06a9\u0631\u062f\u0646 -python-04.png\" title=\"\"><\/p>\n<p>\u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0647\u0645\u0627\u0646 \u0645\u0646\u0637\u0642\u060c \u062f\u0631 \u0628\u0642\u06cc\u0647 \u0645\u0648\u0627\u0631\u062f \u062d\u0631\u06a9\u062a \u0645\u06cc \u06a9\u0646\u06cc\u0645 \u0648 \u062f\u0631 \u0646\u0647\u0627\u06cc\u062a \u0628\u0627 \u0622\u0631\u0627\u06cc\u0647 \u0627\u06cc \u0627\u0632 <code>(1, 2, 3, 4, 7, 8, 11)<\/code>.<\/p>\n<p>\u0627\u06cc\u0646 <em>\u062f\u0648 \u0645\u0648\u0631\u062f \u062e\u0627\u0635<\/em> \u06a9\u0647 \u0645\u0645\u06a9\u0646 \u0627\u0633\u062a \u0631\u062e \u062f\u0647\u062f \u0639\u0628\u0627\u0631\u062a\u0646\u062f \u0627\u0632:<\/p>\n<ul>\n<li>\u0647\u0631 \u062f\u0648 \u0632\u06cc\u0631\u0622\u0631\u0627\u06cc\u0647 \u062f\u0627\u0631\u0627\u06cc \u06cc\u06a9 \u0639\u0646\u0635\u0631 \u0647\u0633\u062a\u0646\u062f.  \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u06cc\u0645 \u062f\u0631 \u0647\u0631 \u06cc\u06a9 \u0628\u0647 \u062c\u0644\u0648 \u062d\u0631\u06a9\u062a \u06a9\u0646\u06cc\u0645 \u0648 \u0639\u0646\u0635\u0631 \u0631\u0627 \u0628\u0647 \u0622\u0631\u0627\u06cc\u0647 \u0645\u0631\u062a\u0628\u200c\u0634\u062f\u0647 \u0627\u0636\u0627\u0641\u0647 \u06a9\u0646\u06cc\u0645.  \u0627\u0632 \u0646\u0638\u0631 \u0641\u0646\u06cc \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u06cc\u0645 \u062f\u0631 \u0647\u0631 \u062f\u0648 \u0622\u0631\u0627\u06cc\u0647 \u0628\u0647 \u062c\u0644\u0648 \u062d\u0631\u06a9\u062a \u06a9\u0646\u06cc\u0645 \u0648 \u0647\u0631 \u062f\u0648 \u0639\u0646\u0635\u0631 \u0631\u0627 \u0628\u0647 \u0622\u0631\u0627\u06cc\u0647 \u0645\u0631\u062a\u0628\u200c\u0634\u062f\u0647 \u0627\u0636\u0627\u0641\u0647 \u06a9\u0646\u06cc\u0645\u060c \u0627\u0645\u0627 \u0632\u0645\u0627\u0646\u06cc \u06a9\u0647 \u0628\u0627 \u0639\u0646\u0627\u0635\u0631 \u0645\u0634\u0627\u0628\u0647 \u062f\u0631 \u0647\u0631 \u062f\u0648 \u0622\u0631\u0627\u06cc\u0647 \u0645\u0648\u0627\u062c\u0647 \u0645\u06cc\u200c\u0634\u0648\u06cc\u0645\u060c \u0627\u06cc\u0646 \u06a9\u0627\u0631 \u0628\u0647 \u0631\u0641\u062a\u0627\u0631 \u062e\u0627\u0635\u06cc \u0646\u06cc\u0627\u0632 \u062f\u0627\u0631\u062f.<\/li>\n<li>\u0645\u0627 \u0639\u0646\u0627\u0635\u0631 \u0631\u0627 \u062f\u0631 \u06cc\u06a9 \u0632\u06cc\u0631\u0622\u0631\u0627\u06cc\u0647 &#8220;\u062a\u0645\u0627\u0645&#8221; \u0645\u06cc \u06a9\u0646\u06cc\u0645.  \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u0645\u062b\u0627\u0644\u060c \u06cc\u06a9 \u0622\u0631\u0627\u06cc\u0647 \u0628\u0627 {1\u060c 2\u060c 3} \u0648 \u06cc\u06a9 \u0622\u0631\u0627\u06cc\u0647 \u0628\u0627 {9\u060c 10\u060c 11} \u062f\u0627\u0631\u06cc\u0645.  \u0648\u0627\u0636\u062d \u0627\u0633\u062a \u06a9\u0647 \u0645\u0627 \u062a\u0645\u0627\u0645 \u0639\u0646\u0627\u0635\u0631 \u0622\u0631\u0627\u06cc\u0647 \u0627\u0648\u0644 \u0631\u0627 \u0628\u062f\u0648\u0646 \u062d\u0631\u06a9\u062a \u0628\u0647 \u062c\u0644\u0648 \u062d\u062a\u06cc \u06cc\u06a9 \u0628\u0627\u0631 \u062f\u0631 \u0622\u0631\u0627\u06cc\u0647 \u062f\u0648\u0645 \u0645\u0631\u0648\u0631 \u062e\u0648\u0627\u0647\u06cc\u0645 \u06a9\u0631\u062f.  \u0647\u0631 \u0632\u0645\u0627\u0646 \u06a9\u0647 \u062f\u0631 \u06cc\u06a9 \u0632\u06cc\u0631\u0622\u0631\u0627\u06cc\u0647 \u0627\u0632 \u0639\u0646\u0627\u0635\u0631 \u06a9\u0645 \u06a9\u0646\u06cc\u0645\u060c \u0628\u0647 \u0633\u0627\u062f\u06af\u06cc \u0639\u0646\u0627\u0635\u0631 \u062f\u0648\u0645 \u0631\u0627 \u06cc\u06a9\u06cc \u067e\u0633 \u0627\u0632 \u062f\u06cc\u06af\u0631\u06cc \u0627\u0636\u0627\u0641\u0647 \u0645\u06cc \u06a9\u0646\u06cc\u0645.<\/li>\n<\/ul>\n<div class=\"alert alert-note\">\n<div class=\"flex\">\n<div class=\"flex-shrink-0 mr-3\"><\/div>\n<div class=\"w-full\">\n<p><strong>\u062a\u0648\u062c\u0647 \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u06cc\u062f:<\/strong> \u0628\u0647 \u062e\u0627\u0637\u0631 \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u06cc\u062f \u06a9\u0647 \u0645\u0627 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u06cc\u0645 \u0647\u0631 \u0637\u0648\u0631 \u06a9\u0647 \u0645\u06cc\u200c\u062e\u0648\u0627\u0647\u06cc\u0645 \u0645\u0631\u062a\u0628 \u06a9\u0646\u06cc\u0645 &#8211; \u0627\u06cc\u0646 \u0645\u062b\u0627\u0644 \u0627\u0639\u062f\u0627\u062f \u0635\u062d\u06cc\u062d \u0631\u0627 \u0628\u0647 \u062a\u0631\u062a\u06cc\u0628 \u0635\u0639\u0648\u062f\u06cc \u0645\u0631\u062a\u0628 \u0645\u06cc\u200c\u06a9\u0646\u062f\u060c \u0627\u0645\u0627 \u0628\u0647 \u0647\u0645\u06cc\u0646 \u0631\u0627\u062d\u062a\u06cc \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u06cc\u0645 \u0628\u0647 \u062a\u0631\u062a\u06cc\u0628 \u0646\u0632\u0648\u0644\u06cc \u06cc\u0627 \u0627\u0634\u06cc\u0627\u0621 \u0633\u0641\u0627\u0631\u0634\u06cc \u0631\u0627 \u0645\u0631\u062a\u0628 \u06a9\u0646\u06cc\u0645.<\/p>\n<\/p><\/div><\/div><\/div>\n<h3 id=\"howtoimplementmergesortinpython\"><span class=\"ez-toc-section\" id=\"%d8%b1%d9%88%d8%b4_%d9%be%db%8c%d8%a7%d8%af%d9%87_%d8%b3%d8%a7%d8%b2%db%8c_merge_sort_%d8%af%d8%b1_%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86\"><\/span>\u0631\u0648\u0634 \u067e\u06cc\u0627\u062f\u0647 \u0633\u0627\u0632\u06cc Merge Sort \u062f\u0631 \u067e\u0627\u06cc\u062a\u0648\u0646<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u0645\u0631\u062a\u0628 \u0633\u0627\u0632\u06cc \u0627\u062f\u063a\u0627\u0645 \u0631\u0627 \u0627\u062c\u0631\u0627 \u062e\u0648\u0627\u0647\u06cc\u0645 \u06a9\u0631\u062f \u0631\u0648\u06cc \u062f\u0648 \u0646\u0648\u0639 \u0645\u062c\u0645\u0648\u0639\u0647 &#8211; \u0631\u0648\u06cc \u0622\u0631\u0627\u06cc\u0647 \u0647\u0627\u06cc \u0627\u0639\u062f\u0627\u062f \u0635\u062d\u06cc\u062d (\u0645\u0639\u0645\u0648\u0644\u0627\u064b \u0628\u0631\u0627\u06cc \u0645\u0639\u0631\u0641\u06cc \u0645\u0631\u062a\u0628 \u0633\u0627\u0632\u06cc \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc \u0634\u0648\u062f) \u0648 \u0631\u0648\u06cc \u0627\u0634\u06cc\u0627\u0621 \u0633\u0641\u0627\u0631\u0634\u06cc (\u0633\u0646\u0627\u0631\u06cc\u0648\u06cc \u0639\u0645\u0644\u06cc \u062a\u0631 \u0648 \u0648\u0627\u0642\u0639\u06cc \u062a\u0631).<\/p>\n<p>\u0645\u0627 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 Merge Sort \u0631\u0627 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 <em>\u0628\u0627\u0644\u0627 \u067e\u0627\u06cc\u06cc\u0646<\/em> \u0631\u0648\u06cc\u06a9\u0631\u062f.  \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u062e\u06cc\u0644\u06cc &#8220;\u0632\u06cc\u0628\u0627&#8221; \u0628\u0647 \u0646\u0638\u0631 \u0646\u0645\u06cc \u0631\u0633\u062f \u0648 \u0645\u06cc \u062a\u0648\u0627\u0646\u062f \u06af\u06cc\u062c \u06a9\u0646\u0646\u062f\u0647 \u0628\u0627\u0634\u062f\u060c \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646 \u0645\u0627 \u0647\u0631 \u0645\u0631\u062d\u0644\u0647 \u0631\u0627 \u0628\u0627 \u062c\u0632\u0626\u06cc\u0627\u062a \u0645\u0631\u0648\u0631 \u062e\u0648\u0627\u0647\u06cc\u0645 \u06a9\u0631\u062f.<\/p>\n<h4 id=\"sortingarrays\">\u0645\u0631\u062a\u0628 \u0633\u0627\u0632\u06cc \u0622\u0631\u0627\u06cc\u0647 \u0647\u0627<\/h4>\n<p>\u0628\u06cc\u0627\u06cc\u06cc\u062f \u0628\u0627 \u0628\u062e\u0634 \u0622\u0633\u0627\u0646 \u0634\u0631\u0648\u0639 \u06a9\u0646\u06cc\u0645.  \u0627\u06cc\u062f\u0647 \u0627\u0635\u0644\u06cc \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0627\u06cc\u0646 \u0627\u0633\u062a \u06a9\u0647 \u0622\u0631\u0627\u06cc\u0647 \u0647\u0627\u06cc (\u0632\u06cc\u0631) \u0631\u0627 \u0628\u0647 \u062f\u0648 \u0646\u06cc\u0645 \u062a\u0642\u0633\u06cc\u0645 \u06a9\u0631\u062f\u0647 \u0648 \u0622\u0646\u0647\u0627 \u0631\u0627 \u0628\u0647 \u0635\u0648\u0631\u062a \u0628\u0627\u0632\u06af\u0634\u062a\u06cc \u0645\u0631\u062a\u0628 \u06a9\u0646\u06cc\u0645.  \u0645\u0627 \u0645\u06cc\u200c\u062e\u0648\u0627\u0647\u06cc\u0645 \u0627\u06cc\u0646 \u06a9\u0627\u0631 \u0631\u0627 \u062a\u0627 \u062d\u062f \u0627\u0645\u06a9\u0627\u0646 \u0627\u062f\u0627\u0645\u0647 \u062f\u0647\u06cc\u0645\u060c \u06cc\u0639\u0646\u06cc \u062a\u0627 \u0632\u0645\u0627\u0646\u06cc \u06a9\u0647 \u0628\u0647 \u0632\u06cc\u0631\u0622\u0631\u0627\u06cc\u0647\u200c\u0647\u0627\u06cc\u06cc \u0628\u0631\u0633\u06cc\u0645 \u06a9\u0647 \u0641\u0642\u0637 \u06cc\u06a9 \u0639\u0646\u0635\u0631 \u062f\u0627\u0631\u0646\u062f:<\/p>\n<pre><code class=\"hljs\"><span class=\"hljs-function\"><span class=\"hljs-keyword\">def<\/span> <span class=\"hljs-title\">merge_sort<\/span>(<span class=\"hljs-params\">array, left_index, right_index<\/span>):<\/span>\n    <span class=\"hljs-keyword\">if<\/span> left_index &gt;= right_index:\n        <span class=\"hljs-keyword\">return<\/span>\n\n    middle = (left_index + right_index)\/\/<span class=\"hljs-number\">2<\/span>\n    merge_sort(array, left_index, middle)\n    merge_sort(array, middle + <span class=\"hljs-number\">1<\/span>, right_index)\n    merge(array, left_index, right_index, middle)\n<\/code><\/pre>\n<p>\u0628\u0627 \u062a\u0645\u0627\u0633 \u0628\u0627 <code>merge<\/code> \u0631\u0648\u0634 \u0622\u062e\u0631\u060c \u0645\u0627 \u0645\u0637\u0645\u0626\u0646 \u0645\u06cc \u0634\u0648\u06cc\u0645 \u06a9\u0647 \u0642\u0628\u0644 \u0627\u0632 \u0634\u0631\u0648\u0639 \u0645\u0631\u062a\u0628 \u0633\u0627\u0632\u06cc\u060c \u062a\u0645\u0627\u0645 \u062a\u0642\u0633\u06cc\u0645\u0627\u062a \u0627\u062a\u0641\u0627\u0642 \u0645\u06cc \u0627\u0641\u062a\u062f.  \u0645\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc \u06a9\u0646\u06cc\u0645 <code>\/\/<\/code> \u0639\u0645\u0644\u06af\u0631 \u0628\u0647 \u0635\u0631\u0627\u062d\u062a \u062f\u0631 \u0645\u0648\u0631\u062f \u0627\u06cc\u0646 \u0648\u0627\u0642\u0639\u06cc\u062a \u0627\u0633\u062a \u06a9\u0647 \u0645\u0627 \u0645\u0642\u0627\u062f\u06cc\u0631 \u0635\u062d\u06cc\u062d \u0628\u0631\u0627\u06cc \u0634\u0627\u062e\u0635 \u0647\u0627\u06cc \u062e\u0648\u062f \u0645\u06cc \u062e\u0648\u0627\u0647\u06cc\u0645.<\/p>\n<p>\u0645\u0631\u062d\u0644\u0647 \u0628\u0639\u062f\u06cc \u0628\u062e\u0634 \u0627\u062f\u063a\u0627\u0645 \u0648\u0627\u0642\u0639\u06cc \u0627\u0632 \u0637\u0631\u06cc\u0642 \u0686\u0646\u062f \u0645\u0631\u062d\u0644\u0647 \u0648 \u0633\u0646\u0627\u0631\u06cc\u0648 \u0627\u0633\u062a:<\/p>\n<ul>\n<li>\u0627\u0632 \u0622\u0631\u0627\u06cc\u0647 \u0647\u0627\u06cc \u0645\u0627 \u06a9\u067e\u06cc \u0627\u06cc\u062c\u0627\u062f \u06a9\u0646\u06cc\u062f.  \u0627\u0648\u0644\u06cc\u0646 \u0622\u0631\u0627\u06cc\u0647 \u0632\u06cc\u0631\u0622\u0631\u0627\u06cc\u0647 \u0627\u0632 \u0627\u0633\u062a <code>(left_index,..,middle)<\/code> \u0648 \u062f\u0648\u0645\u06cc \u0627\u0632 <code>(middle+1,...,right_index)<\/code><\/li>\n<li>\u0645\u0627 \u0627\u0632 \u0647\u0631 \u062f\u0648 \u0646\u0633\u062e\u0647 \u0639\u0628\u0648\u0631 \u0645\u06cc \u06a9\u0646\u06cc\u0645 (\u0631\u062f\u06cc\u0627\u0628\u06cc \u0646\u0634\u0627\u0646\u06af\u0631\u0647\u0627 \u062f\u0631 \u0647\u0631 \u062f\u0648 \u0622\u0631\u0627\u06cc\u0647)\u060c \u0627\u0632 \u0628\u06cc\u0646 \u062f\u0648 \u0639\u0646\u0635\u0631\u06cc \u06a9\u0647 \u062f\u0631 \u062d\u0627\u0644 \u062d\u0627\u0636\u0631 \u0628\u0647 \u0622\u0646\u0647\u0627 \u0646\u06af\u0627\u0647 \u0645\u06cc \u06a9\u0646\u06cc\u0645\u060c \u06a9\u0648\u0686\u06a9\u062a\u0631 \u0631\u0627 \u0627\u0646\u062a\u062e\u0627\u0628 \u0645\u06cc \u06a9\u0646\u06cc\u0645 \u0648 \u0622\u0646\u0647\u0627 \u0631\u0627 \u0628\u0647 \u0622\u0631\u0627\u06cc\u0647 \u0645\u0631\u062a\u0628 \u0634\u062f\u0647 \u062e\u0648\u062f \u0627\u0636\u0627\u0641\u0647 \u0645\u06cc \u06a9\u0646\u06cc\u0645.  \u062f\u0631 \u0647\u0631 \u0622\u0631\u0627\u06cc\u0647 \u0627\u06cc \u06a9\u0647 \u0639\u0646\u0635\u0631 \u0631\u0627 \u0627\u0646\u062a\u062e\u0627\u0628 \u06a9\u0631\u062f\u0647 \u0627\u06cc\u0645 \u0628\u0647 \u062c\u0644\u0648 \u062d\u0631\u06a9\u062a \u0645\u06cc \u06a9\u0646\u06cc\u0645 \u0648 \u0628\u062f\u0648\u0646 \u062a\u0648\u062c\u0647 \u0628\u0647 \u0622\u0631\u0627\u06cc\u0647 \u0645\u0631\u062a\u0628 \u0634\u062f\u0647 \u0628\u0647 \u062c\u0644\u0648 \u0645\u06cc \u0631\u0648\u06cc\u0645.<\/li>\n<li>\u0627\u06af\u0631 \u062f\u0631 \u06cc\u06a9\u06cc \u0627\u0632 \u06a9\u067e\u06cc\u200c\u0647\u0627\u06cc\u0645\u0627\u0646 \u0639\u0646\u0627\u0635\u0631 \u0645\u0627 \u062a\u0645\u0627\u0645 \u0634\u062f &#8211; \u0628\u0647 \u0633\u0627\u062f\u06af\u06cc \u0639\u0646\u0627\u0635\u0631 \u0628\u0627\u0642\u06cc\u200c\u0645\u0627\u0646\u062f\u0647 \u062f\u0631 \u06a9\u067e\u06cc \u062f\u06cc\u06af\u0631 \u0631\u0627 \u0628\u0647 \u0622\u0631\u0627\u06cc\u0647 \u0645\u0631\u062a\u0628 \u0634\u062f\u0647 \u0627\u0636\u0627\u0641\u0647 \u06a9\u0646\u06cc\u062f.<\/li>\n<\/ul>\n<p>\u0628\u0627 \u062a\u0648\u062c\u0647 \u0628\u0647 \u0627\u0644\u0632\u0627\u0645\u0627\u062a \u0645\u0627\u060c \u0628\u06cc\u0627\u06cc\u06cc\u062f \u062c\u0644\u0648 \u0628\u0631\u0648\u06cc\u0645 \u0648 a \u0631\u0627 \u062a\u0639\u0631\u06cc\u0641 \u06a9\u0646\u06cc\u0645 <code>merge()<\/code> \u062a\u0627\u0628\u0639:<\/p>\n<pre><code class=\"hljs\"><span class=\"hljs-function\"><span class=\"hljs-keyword\">def<\/span> <span class=\"hljs-title\">merge<\/span>(<span class=\"hljs-params\">array, left_index, right_index, middle<\/span>):<\/span>\n    \n\n    \n    left_copy = array(left_index:middle + <span class=\"hljs-number\">1<\/span>)\n    right_copy = array(middle+<span class=\"hljs-number\">1<\/span>:right_index+<span class=\"hljs-number\">1<\/span>)\n\n    \n    \n    left_copy_index = <span class=\"hljs-number\">0<\/span>\n    right_copy_index = <span class=\"hljs-number\">0<\/span>\n    sorted_index = left_index\n\n    \n    <span class=\"hljs-keyword\">while<\/span> left_copy_index &lt; <span class=\"hljs-built_in\">len<\/span>(left_copy) <span class=\"hljs-keyword\">and<\/span> right_copy_index &lt; <span class=\"hljs-built_in\">len<\/span>(right_copy):\n\n        \n        \n        <span class=\"hljs-keyword\">if<\/span> left_copy(left_copy_index) &lt;= right_copy(right_copy_index):\n            array(sorted_index) = left_copy(left_copy_index)\n            left_copy_index = left_copy_index + <span class=\"hljs-number\">1<\/span>\n        \n        <span class=\"hljs-keyword\">else<\/span>:\n            array(sorted_index) = right_copy(right_copy_index)\n            right_copy_index = right_copy_index + <span class=\"hljs-number\">1<\/span>\n\n        \n        \n        sorted_index = sorted_index + <span class=\"hljs-number\">1<\/span>\n\n    \n    \n    <span class=\"hljs-keyword\">while<\/span> left_copy_index &lt; <span class=\"hljs-built_in\">len<\/span>(left_copy):\n        array(sorted_index) = left_copy(left_copy_index)\n        left_copy_index = left_copy_index + <span class=\"hljs-number\">1<\/span>\n        sorted_index = sorted_index + <span class=\"hljs-number\">1<\/span>\n\n    <span class=\"hljs-keyword\">while<\/span> right_copy_index &lt; <span class=\"hljs-built_in\">len<\/span>(right_copy):\n        array(sorted_index) = right_copy(right_copy_index)\n        right_copy_index = right_copy_index + <span class=\"hljs-number\">1<\/span>\n        sorted_index = sorted_index + <span class=\"hljs-number\">1<\/span>\n<\/code><\/pre>\n<p>\u062d\u0627\u0644\u0627 \u0628\u06cc\u0627\u06cc\u06cc\u062f \u0628\u0631\u0646\u0627\u0645\u0647 \u062e\u0648\u062f \u0631\u0627 \u0622\u0632\u0645\u0627\u06cc\u0634 \u06a9\u0646\u06cc\u0645:<\/p>\n<pre><code class=\"hljs\">array = (<span class=\"hljs-number\">33<\/span>, <span class=\"hljs-number\">42<\/span>, <span class=\"hljs-number\">9<\/span>, <span class=\"hljs-number\">37<\/span>, <span class=\"hljs-number\">8<\/span>, <span class=\"hljs-number\">47<\/span>, <span class=\"hljs-number\">5<\/span>, <span class=\"hljs-number\">29<\/span>, <span class=\"hljs-number\">49<\/span>, <span class=\"hljs-number\">31<\/span>, <span class=\"hljs-number\">4<\/span>, <span class=\"hljs-number\">48<\/span>, <span class=\"hljs-number\">16<\/span>, <span class=\"hljs-number\">22<\/span>, <span class=\"hljs-number\">26<\/span>)\nmerge_sort(array, <span class=\"hljs-number\">0<\/span>, <span class=\"hljs-built_in\">len<\/span>(array) -<span class=\"hljs-number\">1<\/span>)\n<span class=\"hljs-built_in\">print<\/span>(array)\n<\/code><\/pre>\n<p>\u062e\u0631\u0648\u062c\u06cc \u0627\u06cc\u0646 \u0627\u0633\u062a:<\/p>\n<pre><code class=\"hljs\">(4, 5, 8, 9, 16, 22, 26, 29, 31, 33, 37, 42, 47, 48, 49)\n<\/code><\/pre>\n<h4 id=\"sortingcustomobjects\">\u0645\u0631\u062a\u0628 \u0633\u0627\u0632\u06cc \u0627\u0634\u06cc\u0627\u0621 \u0633\u0641\u0627\u0631\u0634\u06cc<\/h4>\n<p>\u0627\u06a9\u0646\u0648\u0646 \u06a9\u0647 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0627\u0635\u0644\u06cc \u0631\u0627 \u062f\u0631 \u0627\u062e\u062a\u06cc\u0627\u0631 \u062f\u0627\u0631\u06cc\u0645\u060c \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u06cc\u0645 \u0646\u06af\u0627\u0647\u06cc \u0628\u0647 \u0631\u0648\u0634 \u0645\u0631\u062a\u0628\u200c\u0633\u0627\u0632\u06cc \u06a9\u0644\u0627\u0633\u200c\u0647\u0627\u06cc \u0633\u0641\u0627\u0631\u0634\u06cc \u0628\u06cc\u0646\u062f\u0627\u0632\u06cc\u0645.  \u0645\u0627 \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u0645 \u0646\u0627\u062f\u06cc\u062f\u0647 \u0628\u06af\u06cc\u0631\u06cc\u0645 <code>__eq__<\/code>\u060c <code>__le__<\/code>\u060c <code>__ge__<\/code>\u0648 \u0633\u0627\u06cc\u0631 \u0627\u067e\u0631\u0627\u062a\u0648\u0631\u0647\u0627 \u062f\u0631 \u0635\u0648\u0631\u062a \u0646\u06cc\u0627\u0632 \u0628\u0631\u0627\u06cc \u0627\u06cc\u0646 \u06a9\u0627\u0631.<\/p>\n<p>\u0627\u06cc\u0646 \u0628\u0647 \u0645\u0627 \u0627\u0645\u06a9\u0627\u0646 \u0645\u06cc \u062f\u0647\u062f \u0627\u0632 \u0647\u0645\u0627\u0646 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0641\u0648\u0642 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u06a9\u0646\u06cc\u0645\u060c \u0627\u0645\u0627 \u0645\u0627 \u0631\u0627 \u0628\u0647 \u062a\u0646\u0647\u0627 \u06cc\u06a9 \u0631\u0627\u0647 \u0628\u0631\u0627\u06cc \u0645\u0631\u062a\u0628 \u0633\u0627\u0632\u06cc \u0627\u0634\u06cc\u0627\u0621 \u0633\u0641\u0627\u0631\u0634\u06cc \u0645\u062d\u062f\u0648\u062f \u0645\u06cc \u06a9\u0646\u062f\u060c \u06a9\u0647 \u062f\u0631 \u0628\u06cc\u0634\u062a\u0631 \u0645\u0648\u0627\u0631\u062f \u0622\u0646 \u0686\u06cc\u0632\u06cc \u0646\u06cc\u0633\u062a \u06a9\u0647 \u0645\u0627 \u0645\u06cc \u062e\u0648\u0627\u0647\u06cc\u0645.  \u0627\u06cc\u062f\u0647 \u0628\u0647\u062a\u0631 \u0627\u06cc\u0646 \u0627\u0633\u062a \u06a9\u0647 \u062e\u0648\u062f \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0631\u0627 \u0645\u062a\u0646\u0648\u0639 \u062a\u0631 \u06a9\u0646\u06cc\u062f \u0648 \u0628\u0647 \u062c\u0627\u06cc \u0622\u0646 \u06cc\u06a9 \u062a\u0627\u0628\u0639 \u0645\u0642\u0627\u06cc\u0633\u0647 \u0631\u0627 \u0628\u0647 \u0622\u0646 \u0645\u0646\u062a\u0642\u0644 \u06a9\u0646\u06cc\u062f.<\/p>\n<p>\u0627\u0628\u062a\u062f\u0627 \u06cc\u06a9 \u0633\u0641\u0627\u0631\u0634\u06cc \u0631\u0627 \u067e\u06cc\u0627\u062f\u0647 \u0633\u0627\u0632\u06cc \u0645\u06cc \u06a9\u0646\u06cc\u0645 <code>Car<\/code> \u06a9\u0644\u0627\u0633 \u0648 \u0686\u0646\u062f \u0641\u06cc\u0644\u062f \u0628\u0647 \u0622\u0646 \u0627\u0636\u0627\u0641\u0647 \u06a9\u0646\u06cc\u062f:<\/p>\n<pre><code class=\"hljs\"><span class=\"hljs-class\"><span class=\"hljs-keyword\">class<\/span> <span class=\"hljs-title\">Car<\/span>:<\/span>\n    <span class=\"hljs-function\"><span class=\"hljs-keyword\">def<\/span> <span class=\"hljs-title\">__init__<\/span>(<span class=\"hljs-params\">self, make, model, year<\/span>):<\/span>\n        self.make = make\n        self.model = model\n        self.year = year\n\n    <span class=\"hljs-function\"><span class=\"hljs-keyword\">def<\/span> <span class=\"hljs-title\">__str__<\/span>(<span class=\"hljs-params\">self<\/span>):<\/span>\n        <span class=\"hljs-keyword\">return<\/span> <span class=\"hljs-built_in\">str<\/span>.<span class=\"hljs-built_in\">format<\/span>(<span class=\"hljs-string\">\"Make: {}, Model: {}, Year: {}\"<\/span>, self.make, self.model, self.year)\n<\/code><\/pre>\n<p>\u0633\u067e\u0633 \u0686\u0646\u062f \u062a\u063a\u06cc\u06cc\u0631 \u062f\u0631 \u0631\u0648\u0634\u200c\u0647\u0627\u06cc \u0645\u0631\u062a\u0628\u200c\u0633\u0627\u0632\u06cc \u0627\u062f\u063a\u0627\u0645 \u0627\u06cc\u062c\u0627\u062f \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645.  \u0633\u0627\u062f\u0647 \u062a\u0631\u06cc\u0646 \u0631\u0627\u0647 \u0628\u0631\u0627\u06cc \u0631\u0633\u06cc\u062f\u0646 \u0628\u0647 \u0622\u0646\u0686\u0647 \u0645\u06cc \u062e\u0648\u0627\u0647\u06cc\u0645 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u062a\u0648\u0627\u0628\u0639 \u0644\u0627\u0645\u0628\u062f\u0627 \u0627\u0633\u062a.  \u0645\u06cc \u0628\u06cc\u0646\u06cc\u062f \u06a9\u0647 \u0645\u0627 \u0641\u0642\u0637 \u06cc\u06a9 \u067e\u0627\u0631\u0627\u0645\u062a\u0631 \u0627\u0636\u0627\u0641\u06cc \u0627\u0636\u0627\u0641\u0647 \u06a9\u0631\u062f\u06cc\u0645 \u0648 \u0641\u0631\u0627\u062e\u0648\u0627\u0646\u06cc \u0647\u0627\u06cc \u0645\u062a\u062f \u0631\u0627 \u0628\u0631 \u0627\u06cc\u0646 \u0627\u0633\u0627\u0633 \u062a\u063a\u06cc\u06cc\u0631 \u062f\u0627\u062f\u06cc\u0645 \u0648 \u0641\u0642\u0637 \u06cc\u06a9 \u062e\u0637 \u06a9\u062f \u062f\u06cc\u06af\u0631 \u0631\u0627 \u062a\u063a\u06cc\u06cc\u0631 \u062f\u0627\u062f\u06cc\u0645 \u062a\u0627 \u0627\u06cc\u0646 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0628\u0633\u06cc\u0627\u0631 \u0645\u062a\u0646\u0648\u0639 \u062a\u0631 \u0634\u0648\u062f:<\/p>\n<pre><code class=\"hljs\"><span class=\"hljs-function\"><span class=\"hljs-keyword\">def<\/span> <span class=\"hljs-title\">merge<\/span>(<span class=\"hljs-params\">array, left_index, right_index, middle, comparison_function<\/span>):<\/span>\n    left_copy = array(left_index:middle + <span class=\"hljs-number\">1<\/span>)\n    right_copy = array(middle+<span class=\"hljs-number\">1<\/span>:right_index+<span class=\"hljs-number\">1<\/span>)\n\n    left_copy_index = <span class=\"hljs-number\">0<\/span>\n    right_copy_index = <span class=\"hljs-number\">0<\/span>\n    sorted_index = left_index\n\n    <span class=\"hljs-keyword\">while<\/span> left_copy_index &lt; <span class=\"hljs-built_in\">len<\/span>(left_copy) <span class=\"hljs-keyword\">and<\/span> right_copy_index &lt; <span class=\"hljs-built_in\">len<\/span>(right_copy):\n\n        \n        <span class=\"hljs-keyword\">if<\/span> comparison_function(left_copy(left_copy_index), right_copy(right_copy_index)):\n            array(sorted_index) = left_copy(left_copy_index)\n            left_copy_index = left_copy_index + <span class=\"hljs-number\">1<\/span>\n        <span class=\"hljs-keyword\">else<\/span>:\n            array(sorted_index) = right_copy(right_copy_index)\n            right_copy_index = right_copy_index + <span class=\"hljs-number\">1<\/span>\n\n        sorted_index = sorted_index + <span class=\"hljs-number\">1<\/span>\n\n    <span class=\"hljs-keyword\">while<\/span> left_copy_index &lt; <span class=\"hljs-built_in\">len<\/span>(left_copy):\n        array(sorted_index) = left_copy(left_copy_index)\n        left_copy_index = left_copy_index + <span class=\"hljs-number\">1<\/span>\n        sorted_index = sorted_index + <span class=\"hljs-number\">1<\/span>\n\n    <span class=\"hljs-keyword\">while<\/span> right_copy_index &lt; <span class=\"hljs-built_in\">len<\/span>(right_copy):\n        array(sorted_index) = right_copy(right_copy_index)\n        right_copy_index = right_copy_index + <span class=\"hljs-number\">1<\/span>\n        sorted_index = sorted_index + <span class=\"hljs-number\">1<\/span>\n\n\n<span class=\"hljs-function\"><span class=\"hljs-keyword\">def<\/span> <span class=\"hljs-title\">merge_sort<\/span>(<span class=\"hljs-params\">array, left_index, right_index, comparison_function<\/span>):<\/span>\n    <span class=\"hljs-keyword\">if<\/span> left_index &gt;= right_index:\n        <span class=\"hljs-keyword\">return<\/span>\n\n    middle = (left_index + right_index)\/\/<span class=\"hljs-number\">2<\/span>\n    merge_sort(array, left_index, middle, comparison_function)\n    merge_sort(array, middle + <span class=\"hljs-number\">1<\/span>, right_index, comparison_function)\n    merge(array, left_index, right_index, middle, comparison_function)\n<\/code><\/pre>\n<p>\u0628\u06cc\u0627\u06cc\u06cc\u062f \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0627\u0635\u0644\u0627\u062d \u0634\u062f\u0647 \u062e\u0648\u062f \u0631\u0627 \u0622\u0632\u0645\u0627\u06cc\u0634 \u06a9\u0646\u06cc\u0645 \u0631\u0648\u06cc \u062a\u0639\u062f\u0627\u062f \u06a9\u0645\u06cc <code>Car<\/code> \u0645\u0648\u0627\u0631\u062f:<\/p>\n<pre><code class=\"hljs\">car1 = Car(<span class=\"hljs-string\">\"Alfa Romeo\"<\/span>, <span class=\"hljs-string\">\"33 SportWagon\"<\/span>, <span class=\"hljs-number\">1988<\/span>)\ncar2 = Car(<span class=\"hljs-string\">\"Chevrolet\"<\/span>, <span class=\"hljs-string\">\"Cruze Hatchback\"<\/span>, <span class=\"hljs-number\">2011<\/span>)\ncar3 = Car(<span class=\"hljs-string\">\"Corvette\"<\/span>, <span class=\"hljs-string\">\"C6 Couple\"<\/span>, <span class=\"hljs-number\">2004<\/span>)\ncar4 = Car(<span class=\"hljs-string\">\"Cadillac\"<\/span>, <span class=\"hljs-string\">\"Seville Sedan\"<\/span>, <span class=\"hljs-number\">1995<\/span>)\n\narray = (car1, car2, car3, car4)\n\nmerge_sort(array, <span class=\"hljs-number\">0<\/span>, <span class=\"hljs-built_in\">len<\/span>(array) -<span class=\"hljs-number\">1<\/span>, <span class=\"hljs-keyword\">lambda<\/span> carA, carB: carA.year &lt; carB.year)\n\n<span class=\"hljs-built_in\">print<\/span>(<span class=\"hljs-string\">\"Cars sorted by year:\"<\/span>)\n<span class=\"hljs-keyword\">for<\/span> car <span class=\"hljs-keyword\">in<\/span> array:\n    <span class=\"hljs-built_in\">print<\/span>(car)\n\n<span class=\"hljs-built_in\">print<\/span>()\nmerge_sort(array, <span class=\"hljs-number\">0<\/span>, <span class=\"hljs-built_in\">len<\/span>(array) -<span class=\"hljs-number\">1<\/span>, <span class=\"hljs-keyword\">lambda<\/span> carA, carB: carA.make &lt; carB.make)\n<span class=\"hljs-built_in\">print<\/span>(<span class=\"hljs-string\">\"Cars sorted by make:\"<\/span>)\n<span class=\"hljs-keyword\">for<\/span> car <span class=\"hljs-keyword\">in<\/span> array:\n    <span class=\"hljs-built_in\">print<\/span>(car)\n<\/code><\/pre>\n<p>\u062e\u0631\u0648\u062c\u06cc \u0631\u0627 \u0645\u06cc \u06af\u06cc\u0631\u06cc\u0645:<\/p>\n<pre><code class=\"hljs\">Cars sorted by year:\nMake: Alfa Romeo, Model: 33 SportWagon, Year: 1988\nMake: Cadillac, Model: Seville Sedan, Year: 1995\nMake: Corvette, Model: C6 Couple, Year: 2004\nMake: Chevrolet, Model: Cruze Hatchback, Year: 2011\n\nCars sorted by make:\nMake: Alfa Romeo, Model: 33 SportWagon, Year: 1988\nMake: Cadillac, Model: Seville Sedan, Year: 1995\nMake: Chevrolet, Model: Cruze Hatchback, Year: 2011\nMake: Corvette, Model: C6 Couple, Year: 2004\n<\/code><\/pre>\n<h3 id=\"optimization\">\u0628\u0647\u06cc\u0646\u0647 \u0633\u0627\u0632\u06cc<\/h3>\n<p>\u0628\u06cc\u0627\u06cc\u06cc\u062f \u0628\u0647 \u062a\u0641\u0635\u06cc\u0644 \u062a\u0648\u0636\u06cc\u062d \u062f\u0647\u06cc\u0645 \u0631\u0648\u06cc \u062a\u0641\u0627\u0648\u062a \u0645\u06cc\u0627\u0646 <em>\u0628\u0627\u0644\u0627 \u067e\u0627\u06cc\u06cc\u0646<\/em> \u0648 <em>\u0627\u0632 \u067e\u0627\u06cc\u06cc\u0646 \u0628\u0647 \u0628\u0627\u0644\u0627<\/em> \u0627\u062f\u063a\u0627\u0645 \u0645\u0631\u062a\u0628 \u0633\u0627\u0632\u06cc \u062f\u0631 \u062d\u0627\u0644 \u062d\u0627\u0636\u0631. <em>\u0627\u0632 \u067e\u0627\u06cc\u06cc\u0646 \u0628\u0647 \u0628\u0627\u0644\u0627<\/em> \u0645\u0627\u0646\u0646\u062f \u0646\u06cc\u0645\u0647 \u062f\u0648\u0645 \u06a9\u0627\u0631 \u0645\u06cc \u06a9\u0646\u062f <em>\u0628\u0627\u0644\u0627 \u067e\u0627\u06cc\u06cc\u0646<\/em> \u0631\u0648\u06cc\u06a9\u0631\u062f\u06cc \u06a9\u0647 \u062f\u0631 \u0622\u0646 \u0628\u0647 \u062c\u0627\u06cc \u0641\u0631\u0627\u062e\u0648\u0627\u0646\u06cc \u0628\u0627\u0632\u06af\u0634\u062a\u06cc \u0645\u0631\u062a\u0628 \u0633\u0627\u0632\u06cc \u0631\u0648\u06cc \u0632\u06cc\u0631\u0622\u0631\u0627\u06cc\u0647 \u0647\u0627\u06cc \u0646\u0635\u0641 \u0634\u062f\u0647\u060c \u0645\u0627 \u0628\u0647 \u0637\u0648\u0631 \u0645\u06a9\u0631\u0631 \u0632\u06cc\u0631\u0622\u0631\u0627\u06cc\u0647 \u0647\u0627\u06cc \u0645\u062c\u0627\u0648\u0631 \u0631\u0627 \u0645\u0631\u062a\u0628 \u0645\u06cc \u06a9\u0646\u06cc\u0645.<\/p>\n<blockquote>\n<p>\u06cc\u06a9\u06cc \u0627\u0632 \u06a9\u0627\u0631\u0647\u0627\u06cc\u06cc \u06a9\u0647 \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u0645 \u0628\u0631\u0627\u06cc \u0628\u0647\u0628\u0648\u062f \u0627\u06cc\u0646 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0627\u0646\u062c\u0627\u0645 \u062f\u0647\u06cc\u0645 \u0627\u06cc\u0646 \u0627\u0633\u062a \u06a9\u0647 <strong>\u0628\u0647 \u062c\u0627\u06cc \u0639\u0646\u0627\u0635\u0631 \u062a\u06a9\u060c \u062a\u06a9\u0647 \u0647\u0627\u06cc \u0645\u0631\u062a\u0628 \u0634\u062f\u0647 \u0631\u0627 \u062f\u0631 \u0646\u0638\u0631 \u0628\u06af\u06cc\u0631\u06cc\u062f<\/strong> \u0642\u0628\u0644 \u0627\u0632 \u0634\u06a9\u0633\u062a\u0646 \u0622\u0631\u0627\u06cc\u0647<\/p>\n<\/blockquote>\n<p>\u0627\u06cc\u0646 \u0628\u062f\u0627\u0646 \u0645\u0639\u0646\u06cc \u0627\u0633\u062a \u06a9\u0647 \u0628\u0627 \u062a\u0648\u062c\u0647 \u0628\u0647 \u0622\u0631\u0627\u06cc\u0647 \u0627\u06cc \u0645\u0627\u0646\u0646\u062f <code>(4, 8, 7, 2, 11, 1, 3)<\/code>\u060c \u0628\u0647 \u062c\u0627\u06cc \u062a\u062c\u0632\u06cc\u0647 \u0622\u0646 \u0628\u0647 <code>(4), (8), (7), (2), (11), (1) ,(3)<\/code> &#8211; \u0628\u0647 \u0632\u06cc\u0631\u0622\u0631\u0627\u06cc\u0647 \u0647\u0627\u06cc\u06cc \u062a\u0642\u0633\u06cc\u0645 \u0645\u06cc \u0634\u0648\u062f \u06a9\u0647 \u0645\u0645\u06a9\u0646 \u0627\u0633\u062a \u0642\u0628\u0644\u0627\u064b \u0645\u0631\u062a\u0628 \u0634\u062f\u0647 \u0628\u0627\u0634\u0646\u062f: <code>(4,8), (7), (2,11), (1,3)<\/code>\u060c \u0648 \u0633\u067e\u0633 \u0622\u0646\u0647\u0627 \u0631\u0627 \u0645\u0631\u062a\u0628 \u06a9\u0646\u06cc\u062f.<\/p>\n<p>\u0628\u0627 \u062f\u0627\u062f\u0647\u200c\u0647\u0627\u06cc \u0648\u0627\u0642\u0639\u06cc\u060c \u0645\u0627 \u0627\u063a\u0644\u0628 \u062a\u0639\u062f\u0627\u062f \u0632\u06cc\u0627\u062f\u06cc \u0627\u0632 \u0627\u06cc\u0646 \u0632\u06cc\u0631\u0622\u0631\u0627\u06cc\u0647\u200c\u0647\u0627\u06cc \u0645\u0631\u062a\u0628 \u0634\u062f\u0647\u200c\u0627\u06cc \u062f\u0627\u0631\u06cc\u0645 \u06a9\u0647 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u0646\u062f \u0632\u0645\u0627\u0646 \u0627\u062c\u0631\u0627\u06cc Merge Sort \u0631\u0627 \u0628\u0647\u200c\u0637\u0648\u0631 \u0642\u0627\u0628\u0644 \u062a\u0648\u062c\u0647\u06cc \u06a9\u0648\u062a\u0627\u0647 \u06a9\u0646\u0646\u062f.<\/p>\n<p>\u0646\u06a9\u062a\u0647 \u062f\u06cc\u06af\u0631\u06cc \u06a9\u0647 \u0628\u0627\u06cc\u062f \u0628\u0627 Merge Sort \u062f\u0631 \u0646\u0638\u0631 \u06af\u0631\u0641\u062a\u060c \u0628\u0647 \u0648\u06cc\u0698\u0647 <em>\u0628\u0627\u0644\u0627 \u067e\u0627\u06cc\u06cc\u0646<\/em> \u0646\u0633\u062e\u0647 \u0627\u0633\u062a <strong>\u0686\u0646\u062f \u0631\u0634\u062a\u0647 \u0627\u06cc<\/strong>.  \u0645\u0631\u062a\u0628 \u0633\u0627\u0632\u06cc \u0627\u062f\u063a\u0627\u0645 \u0628\u0631\u0627\u06cc \u0627\u06cc\u0646 \u06a9\u0627\u0631 \u0631\u0627\u062d\u062a \u0627\u0633\u062a \u0632\u06cc\u0631\u0627 \u0647\u0631 \u0646\u06cc\u0645\u0647 \u0645\u06cc \u062a\u0648\u0627\u0646\u062f \u0645\u0633\u062a\u0642\u0644 \u0627\u0632 \u062c\u0641\u062a \u062e\u0648\u062f \u0645\u0631\u062a\u0628 \u0634\u0648\u062f.  \u062a\u0646\u0647\u0627 \u0686\u06cc\u0632\u06cc \u06a9\u0647 \u0628\u0627\u06cc\u062f \u0627\u0632 \u0622\u0646 \u0645\u0637\u0645\u0626\u0646 \u0634\u0648\u06cc\u0645 \u0627\u06cc\u0646 \u0627\u0633\u062a \u06a9\u0647 \u0645\u0631\u062a\u0628 \u0633\u0627\u0632\u06cc \u0647\u0631 \u0646\u06cc\u0645\u0647 \u0642\u0628\u0644 \u0627\u0632 \u0627\u062f\u063a\u0627\u0645 \u0622\u0646\u0647\u0627 \u062a\u0645\u0627\u0645 \u0634\u062f\u0647 \u0627\u0633\u062a.<\/p>\n<p>\u0628\u0627 \u0627\u06cc\u0646 \u062d\u0627\u0644 \u0645\u0631\u062a\u0628 \u0633\u0627\u0632\u06cc \u0627\u062f\u063a\u0627\u0645 \u0646\u0633\u0628\u062a\u0627\u064b \u0646\u0627\u06a9\u0627\u0631\u0622\u0645\u062f \u0627\u0633\u062a (\u0647\u0645 \u062f\u0631 \u0632\u0645\u0627\u0646 \u0648 \u0647\u0645 \u0645\u06a9\u0627\u0646). <em>\u0622\u0631\u0627\u06cc\u0647 \u0647\u0627\u06cc \u06a9\u0648\u0686\u06a9\u062a\u0631<\/em> \u0648 \u0627\u063a\u0644\u0628 \u0628\u0627 \u062a\u0648\u0642\u0641 \u0632\u0645\u0627\u0646\u06cc \u06a9\u0647 \u0628\u0647 \u0622\u0631\u0627\u06cc\u0647 \u0627\u06cc \u0627\u0632 7 \u0639\u0646\u0635\u0631 \u0645\u06cc \u0631\u0633\u06cc\u0645\u060c \u0628\u0647 \u062c\u0627\u06cc \u067e\u0627\u06cc\u06cc\u0646 \u0631\u0641\u062a\u0646 \u0628\u0647 \u0622\u0631\u0627\u06cc\u0647 \u0647\u0627\u06cc \u062f\u0627\u0631\u0627\u06cc \u06cc\u06a9 \u0639\u0646\u0635\u0631\u060c \u0648 \u0641\u0631\u0627\u062e\u0648\u0627\u0646\u06cc Insertion Sort \u0628\u0631\u0627\u06cc \u0645\u0631\u062a\u0628 \u06a9\u0631\u062f\u0646 \u0622\u0646\u0647\u0627\u060c \u0642\u0628\u0644 \u0627\u0632 \u0627\u062f\u063a\u0627\u0645 \u062f\u0631 \u06cc\u06a9 \u0622\u0631\u0627\u06cc\u0647 \u0628\u0632\u0631\u06af\u062a\u0631\u060c \u0628\u0647\u06cc\u0646\u0647 \u0645\u06cc \u0634\u0648\u062f.<\/p>\n<p>\u0627\u06cc\u0646 \u0628\u0647 \u0627\u06cc\u0646 \u062f\u0644\u06cc\u0644 \u0627\u0633\u062a \u06a9\u0647 \u0645\u0631\u062a\u0628 \u0633\u0627\u0632\u06cc \u062f\u0631\u062c \u0628\u0627 \u0622\u0631\u0627\u06cc\u0647 \u0647\u0627\u06cc \u06a9\u0648\u0686\u06a9 \u0648\/\u06cc\u0627 \u062a\u0642\u0631\u06cc\u0628\u0627 \u0645\u0631\u062a\u0628 \u0634\u062f\u0647 \u0628\u0633\u06cc\u0627\u0631 \u062e\u0648\u0628 \u06a9\u0627\u0631 \u0645\u06cc \u06a9\u0646\u062f.<\/p>\n<h3 id=\"conclusion\"><span class=\"ez-toc-section\" id=\"%d9%86%d8%aa%db%8c%d8%ac%d9%87\"><\/span>\u0646\u062a\u06cc\u062c\u0647<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Merge Sort \u06cc\u06a9 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0645\u0631\u062a\u0628 \u0633\u0627\u0632\u06cc \u06a9\u0627\u0631\u0622\u0645\u062f \u0648 \u0647\u0645\u0647 \u0645\u0646\u0638\u0648\u0631\u0647 \u0627\u0633\u062a.  \u0645\u0632\u06cc\u062a \u0627\u0635\u0644\u06cc \u0622\u0646 \u0632\u0645\u0627\u0646 \u0627\u062c\u0631\u0627\u06cc \u0642\u0627\u0628\u0644 \u0627\u0639\u062a\u0645\u0627\u062f \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0648 \u06a9\u0627\u0631\u0627\u06cc\u06cc \u0622\u0646 \u0647\u0646\u06af\u0627\u0645 \u0645\u0631\u062a\u0628 \u0633\u0627\u0632\u06cc \u0622\u0631\u0627\u06cc\u0647 \u0647\u0627\u06cc \u0628\u0632\u0631\u06af \u0627\u0633\u062a.  \u0628\u0631 \u062e\u0644\u0627\u0641 Quick Sort\u060c \u0628\u0647 \u0622\u0646 \u0628\u0633\u062a\u06af\u06cc \u0646\u062f\u0627\u0631\u062f \u0631\u0648\u06cc \u0647\u0631 \u062a\u0635\u0645\u06cc\u0645 \u0646\u0627\u062e\u0648\u0634\u0627\u06cc\u0646\u062f\u06cc \u06a9\u0647 \u0645\u0646\u062c\u0631 \u0628\u0647 \u0632\u0645\u0627\u0646 \u0627\u062c\u0631\u0627 \u0628\u062f \u0634\u0648\u062f.<\/p>\n<p>\u06cc\u06a9\u06cc \u0627\u0632 \u0627\u0634\u06a9\u0627\u0644\u0627\u062a \u0627\u0635\u0644\u06cc \u062d\u0627\u0641\u0638\u0647 \u0627\u0636\u0627\u0641\u06cc \u0627\u0633\u062a \u06a9\u0647 Merge Sort \u0628\u0631\u0627\u06cc \u0630\u062e\u06cc\u0631\u0647 \u06a9\u067e\u06cc \u0647\u0627\u06cc \u0645\u0648\u0642\u062a \u0622\u0631\u0627\u06cc\u0647 \u0647\u0627 \u0642\u0628\u0644 \u0627\u0632 \u0627\u062f\u063a\u0627\u0645 \u0622\u0646\u0647\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc \u06a9\u0646\u062f.  \u0628\u0627 \u0627\u06cc\u0646 \u062d\u0627\u0644\u060c Merge Sort \u06cc\u06a9 \u0645\u062b\u0627\u0644 \u0639\u0627\u0644\u06cc \u0648 \u0634\u0647\u0648\u062f\u06cc \u0628\u0631\u0627\u06cc \u0645\u0639\u0631\u0641\u06cc \u0645\u0647\u0646\u062f\u0633\u0627\u0646 \u0646\u0631\u0645 \u0627\u0641\u0632\u0627\u0631 \u0622\u06cc\u0646\u062f\u0647 \u0628\u0627 \u0631\u0648\u06cc\u06a9\u0631\u062f \u062a\u0642\u0633\u06cc\u0645 \u0648 \u063a\u0644\u0628\u0647 \u0628\u0631\u0627\u06cc \u0627\u06cc\u062c\u0627\u062f \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0627\u0633\u062a.<\/p>\n<p>\u0645\u0627 \u0645\u0631\u062a\u0628 \u0633\u0627\u0632\u06cc \u0627\u062f\u063a\u0627\u0645 \u0647\u0631 \u062f\u0648 \u0631\u0627 \u067e\u06cc\u0627\u062f\u0647 \u0633\u0627\u0632\u06cc \u06a9\u0631\u062f\u0647 \u0627\u06cc\u0645 \u0631\u0648\u06cc \u0622\u0631\u0627\u06cc\u0647 \u0647\u0627\u06cc \u0627\u0639\u062f\u0627\u062f \u0635\u062d\u06cc\u062d \u0633\u0627\u062f\u0647 \u0648 \u0631\u0648\u06cc \u0627\u0634\u06cc\u0627\u0621 \u0633\u0641\u0627\u0631\u0634\u06cc \u0627\u0632 \u0637\u0631\u06cc\u0642 \u062a\u0627\u0628\u0639 \u0644\u0627\u0645\u0628\u062f\u0627 \u06a9\u0647 \u0628\u0631\u0627\u06cc \u0645\u0642\u0627\u06cc\u0633\u0647 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc \u0634\u0648\u062f.  \u062f\u0631 \u067e\u0627\u06cc\u0627\u0646\u060c \u0628\u0647\u06cc\u0646\u0647\u200c\u0633\u0627\u0632\u06cc\u200c\u0647\u0627\u06cc \u0645\u0645\u06a9\u0646 \u0628\u0631\u0627\u06cc \u0647\u0631 \u062f\u0648 \u0631\u0648\u06cc\u06a9\u0631\u062f \u0628\u0647 \u0627\u062e\u062a\u0635\u0627\u0631 \u0645\u0648\u0631\u062f \u0628\u062d\u062b \u0642\u0631\u0627\u0631 \u06af\u0631\u0641\u062a.<\/p>\n<\/div>\n<p><script>\n                        !function(f,b,e,v,n,t,s)\n                        {if(f.fbq)return;n=f.fbq=function(){n.callMethod?\n                        n.callMethod.apply(n,arguments):n.queue.push(arguments)};\n                        if(!f._fbq)f._fbq=n;n.push=n;n.loaded=!0;n.version='2.0';\n                        n.queue=();t=b.createElement(e);t.async=!0;\n                        t.src=v;s=b.getElementsByTagName(e)(0);\n                        s.parentNode.insertBefore(t,s)}(window, document,'script',\n                        'https:\/\/connect.facebook.net\/en_US\/fbevents.js');\n                        fbq('init', '525232124909042');\n                        fbq('track', 'PageView');\n                    <\/script>    (\u0628\u0631\u0686\u0633\u0628\u200c\u0647\u0627 \u0628\u0647 \u062a\u0631\u062c\u0645\u0647)# python<br \/>\n<br \/><br \/>\n<br \/>\u0645\u0646\u062a\u0634\u0631 \u0634\u062f\u0647 \u062f\u0631 1403-01-19 02:37:03<br \/>\n<\/p>\n\n\n<div class=\"kk-star-ratings kksr-auto kksr-align-center kksr-valign-bottom\"\n    data-payload='{&quot;align&quot;:&quot;center&quot;,&quot;id&quot;:&quot;15953&quot;,&quot;slug&quot;:&quot;default&quot;,&quot;valign&quot;:&quot;bottom&quot;,&quot;ignore&quot;:&quot;&quot;,&quot;reference&quot;:&quot;auto&quot;,&quot;class&quot;:&quot;&quot;,&quot;count&quot;:&quot;0&quot;,&quot;legendonly&quot;:&quot;&quot;,&quot;readonly&quot;:&quot;&quot;,&quot;score&quot;:&quot;0&quot;,&quot;starsonly&quot;:&quot;&quot;,&quot;best&quot;:&quot;5&quot;,&quot;gap&quot;:&quot;5&quot;,&quot;greet&quot;:&quot;\u0627\u0645\u062a\u06cc\u0627\u0632 \u0634\u0645\u0627 \u0628\u0647 \u0627\u06cc\u0646 \u0645\u0637\u0644\u0628&quot;,&quot;legend&quot;:&quot;0\\\/5 (0 \u0631\u0627\u06cc)&quot;,&quot;size&quot;:&quot;30&quot;,&quot;title&quot;:&quot;\u0627\u062f\u063a\u0627\u0645 \u0645\u0631\u062a\u0628 \u0633\u0627\u0632\u06cc \u062f\u0631 \u067e\u0627\u06cc\u062a\u0648\u0646&quot;,&quot;width&quot;:&quot;0&quot;,&quot;_legend&quot;:&quot;{score}\\\/{best} ({count} \u0631\u0627\u06cc)&quot;,&quot;font_factor&quot;:&quot;1.25&quot;}'>\n            \n<div class=\"kksr-stars\">\n    \n<div class=\"kksr-stars-inactive\">\n            <div class=\"kksr-star\" data-star=\"1\" style=\"padding-left: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 30px; height: 30px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" data-star=\"2\" style=\"padding-left: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 30px; height: 30px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" data-star=\"3\" style=\"padding-left: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 30px; height: 30px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" data-star=\"4\" style=\"padding-left: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 30px; height: 30px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" data-star=\"5\" style=\"padding-left: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 30px; height: 30px;\"><\/div>\n        <\/div>\n    <\/div>\n    \n<div class=\"kksr-stars-active\" style=\"width: 0px;\">\n            <div class=\"kksr-star\" style=\"padding-left: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 30px; height: 30px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" style=\"padding-left: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 30px; height: 30px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" style=\"padding-left: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 30px; height: 30px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" style=\"padding-left: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 30px; height: 30px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" style=\"padding-left: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 30px; height: 30px;\"><\/div>\n        <\/div>\n    <\/div>\n<\/div>\n                \n\n<div class=\"kksr-legend\" style=\"font-size: 24px;\">\n            <span class=\"kksr-muted\">\u0627\u0645\u062a\u06cc\u0627\u0632 \u0634\u0645\u0627 \u0628\u0647 \u0627\u06cc\u0646 \u0645\u0637\u0644\u0628<\/span>\n    <\/div>\n    <\/div>\n","protected":false},"excerpt":{"rendered":"<p><span class=\"span-reading-time rt-reading-time\" style=\"display: block;\"><span class=\"rt-label rt-prefix\">\u0632\u0645\u0627\u0646 \u0644\u0627\u0632\u0645 \u0628\u0631\u0627\u06cc \u0645\u0637\u0627\u0644\u0639\u0647: <\/span> <span class=\"rt-time\"> 8<\/span> <span class=\"rt-label rt-postfix\">\u062f\u0642\u06cc\u0642\u0647<\/span><\/span>\u0645\u0639\u0631\u0641\u06cc Merge Sort \u06cc\u06a9\u06cc \u0627\u0632 \u0645\u0639\u0631\u0648\u0641 \u062a\u0631\u06cc\u0646 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0647\u0627\u06cc \u0645\u0631\u062a\u0628 \u0633\u0627\u0632\u06cc \u0627\u0633\u062a. 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